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Home » The LCM takes the highest power of each prime: - inBeat

The LCM takes the highest power of each prime: - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Question: An industrial designer offers custom phone cases with 5 color palettes and 4 pattern options. A customer picks exactly 3 different colors and 1 pattern, where the order of colors does not matter. How many unique case designs can be made?

📌 Solution: First, choose 3 different colors from 5, where order does not matter:

📌 Therefore, there are $40$ unique phone case designs possible.

📌 Thus, there are 126 distinct ways to label the vertices.

📌 The distances form an arithmetic sequence:

📌 The average distance over five days is given by:

📌 d_1 + d_1 + 10 + d_1 + 20 + d_1 + 30 + d_1 + 40 = 5d_1 + 100

📌 A GPS tracker on a bird records its altitude over five consecutive hours as an arithmetic sequence. The sum of the altitudes is 1,000 meters, and the highest altitude is 240 meters. Find the common difference of the sequence.

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